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What Is Music? 33the middle of the piano keyboard has been fixed to have a frequency of440 Hz. This is entirely arbitrary. We could fix A at any frequency, such as439, 444, 424, or 314.159; different standards were used in the time ofMozart than today. Some people claim that the precise frequencies affectthe overall sound of a musical piece and the sound of instruments. LedZeppelin often tuned their instruments away from the modern A440 standardto give their music an uncommon sound, and perhaps to link it withthe European children’s folk songs that inspired many of their compositions.Many purists insist on hearing baroque music on period instruments,both because the instruments have a different sound and becausethey are designed to play the music in its original tuning standard, somethingthat purists deem important.We can fix pitches anywhere we want because what defines music isa set of pitch relations. The specific frequencies for notes may be arbitrary,but the distance from one frequency to the next—and hence fromone note to the next in our musical system—isn’t at all arbitrary. Eachnote in our musical system is equally spaced to our ears (but not necessarilyto the ears of other species). Although there is not an equal changein cycles per second (Hz) as we climb from one note to the next, the distancebetween each note and the next sounds equal. How can this be?The frequency of each note in our system is approximately 6 percentmore than the one before it. Our auditory system is sensitive both to relativechanges and to proportional changes in sound. Thus, each increasein frequency of 6 percent gives us the impression that we have increasedpitch by the same amount as we did last time.The idea of proportional change is intuitive if you think aboutweights. If you’re at a gym and you want to increase your weight liftingof the barbells from 5 pounds to 50 pounds, adding 5 pounds each weekis not going to change the amount of weight you’re lifting in an equalway. After a week of lifting 5 pounds, when you move to 10 you are doublingthe weight; the next week when you move to 15 you are adding 1.5times as much weight as you had before. An equal spacing—to give yourmuscles a similar increase of weight each week—would be to add a constantpercentage of the previous week’s weight each time you increase.